Question 444284
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi

Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}}
where Pt(h,k) is the center and a and b  are the respective vertices distances from center.
{{{ (x)^2/4 + (y)^2/9 = 1}}}  and {{{y = -x+3}}} 
 x^2/4 + (x^2 - 6x + 9)/9 = 1
  9x^2 + 4x^2-24x+36 = 36
      13x^2 -24x = 0
     x(13x -24) = 0   x = 0 and x = 24/13  
(0,3)  and (24/13,15/13) the solutions for this system
{{{drawing(300,300,-6, 6, -6, 6,   arc(0,0,4,6),
 grid(1),
circle(0, 3,0.2),
circle(24/13, 15/13,0.2),
graph( 300, 300,-6, 6, -6, 6,0, -x+3 ))}}}